Fermionic SPT phases in higher dimensions and bosonization

Kapustin, Anton; Thorngren, Ryan

doi:10.1007/JHEP10(2017)080

Title: Fermionic SPT phases in higher dimensions and bosonization

Abstract

We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with higher-form symmetries. We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry G. It generalizes the supercohomology of Gu and Wen. We argue that the most general such phase can be obtained from a bosonic “shadow” by condensing both fermionic particles and strings.

Authors:

Kapustin, Anton ^[1]; Thorngren, Ryan ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States)
Univ. of California, Berkeley, CA (United States)

Publication Date:: 2017-10-11

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1597951

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Effective Field Theories; Topological Field Theories; Topological States of Matter

Citation Formats


                    Kapustin, Anton, and Thorngren, Ryan. Fermionic SPT phases in higher dimensions and bosonization.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP10(2017)080.

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                    Kapustin, Anton, & Thorngren, Ryan. Fermionic SPT phases in higher dimensions and bosonization.  United States.  https://doi.org/10.1007/JHEP10(2017)080

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                    Kapustin, Anton, and Thorngren, Ryan. Wed .  
"Fermionic SPT phases in higher dimensions and bosonization".  United States.  https://doi.org/10.1007/JHEP10(2017)080.  https://www.osti.gov/servlets/purl/1597951.

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@article{osti_1597951,

  title        = {Fermionic SPT phases in higher dimensions and bosonization},

  author       = {Kapustin, Anton and Thorngren, Ryan},

  abstractNote = {We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with higher-form symmetries. We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry G. It generalizes the supercohomology of Gu and Wen. We argue that the most general such phase can be obtained from a bosonic “shadow” by condensing both fermionic particles and strings.},

  doi          = {10.1007/JHEP10(2017)080},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 10,

  volume       = 2017,

  place        = {United States},

  year         = {2017},

  month        = {10}

}

Copy to clipboard

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Title: Fermionic SPT phases in higher dimensions and bosonization

Abstract

Citation Formats

Spherical 2-Categories and 4-Manifold Invariants journal, May 1999

Anyons in an exactly solved model and beyond journal, January 2006

Products of Cocycles and Extensions of Mappings journal, April 1947

Symmetry-protected topological phases from decorated domain walls journal, March 2014

Fermion masses without symmetry breaking in two spacetime dimensions journal, July 2015

Riemann surfaces and spin structures journal, January 1971

Framed Wilson operators, fermionic strings, and gravitational anomaly in 4d journal, February 2015

Spin TQFTs and fermionic phases of matter journal, October 2016

Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases journal, September 2016

'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas journal, July 1981

Interacting fermionic symmetry-protected topological phases in two dimensions journal, May 2017

Invariants of 3-manifolds via link polynomials and quantum groups journal, December 1991

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter journal, April 2017

Interacting fermionic topological insulators/superconductors in three dimensions journal, May 2014

(3+1)-TQFTs and topological insulators journal, July 2011

Periodic table for topological insulators and superconductors conference, January 2009

Spin Tqfts and Fermionic Phases of Matter conference, November 2016

Ising anyons in frustration-free Majorana-dimer models journal, September 2016

Pin structures on low-dimensional manifolds book, January 1991

Periodic table for topological insulators and superconductors text, January 2009

(3+1)-TQFTs and Topological Insulators preprint, January 2011

Symmetry protected topological phases from decorated domain walls text, January 2013

Interacting fermionic topological insulators/superconductors in three dimensions text, January 2014

Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d text, January 2014

Fermion masses without symmetry breaking in two spacetime dimensions text, January 2014

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter text, January 2016

Ising Anyons in Frustration-Free Majorana-Dimer Models text, January 2016

Anyons in an exactly solved model and beyond text, January 2005

Spherical 2-categories and 4-manifold invariants text, January 1998

Fermion decoration construction of symmetry-protected trivial order for fermion systems with any symmetry and in any dimension journal, December 2019

Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions journal, January 2019

A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants journal, January 2019

Anomalous Symmetry Protected Topological States in Interacting Fermion Systems journal, November 2019

Fermionic projected entangled-pair states and topological phases journal, December 2017

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms journal, January 2020

Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions journal, May 2018

Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3 + 1 D topological orders for boson systems journal, July 2019

Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions journal, October 2018

Higher-order symmetry-protected topological states for interacting bosons and fermions text, January 2018

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions text, January 2017

Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries text, January 2017

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups text, January 2017

Symmetry Protected Topological phases and Generalized Cohomology text, January 2017

Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions text, January 2018

Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions text, January 2018

Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way text, January 2018

Crystalline topological phases as defect networks text, January 2018

Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems text, January 2018

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms text, January 2018

Spherical 2-Categories and 4-Manifold Invariants
journal, May 1999

Anyons in an exactly solved model and beyond
journal, January 2006

Products of Cocycles and Extensions of Mappings
journal, April 1947

Symmetry-protected topological phases from decorated domain walls
journal, March 2014

Fermion masses without symmetry breaking in two spacetime dimensions
journal, July 2015

Riemann surfaces and spin structures
journal, January 1971

Framed Wilson operators, fermionic strings, and gravitational anomaly in 4d
journal, February 2015

Spin TQFTs and fermionic phases of matter
journal, October 2016

Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases
journal, September 2016

'Luttinger liquid theory' of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas
journal, July 1981

Interacting fermionic symmetry-protected topological phases in two dimensions
journal, May 2017

Invariants of 3-manifolds via link polynomials and quantum groups
journal, December 1991

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
journal, April 2017

Interacting fermionic topological insulators/superconductors in three dimensions
journal, May 2014

(3+1)-TQFTs and topological insulators
journal, July 2011

Periodic table for topological insulators and superconductors
conference, January 2009

Spin Tqfts and Fermionic Phases of Matter
conference, November 2016

Ising anyons in frustration-free Majorana-dimer models
journal, September 2016

Pin structures on low-dimensional manifolds
book, January 1991

Periodic table for topological insulators and superconductors
text, January 2009

(3+1)-TQFTs and Topological Insulators
preprint, January 2011

Symmetry protected topological phases from decorated domain walls
text, January 2013

Interacting fermionic topological insulators/superconductors in three dimensions
text, January 2014

Framed Wilson Operators, Fermionic Strings, and Gravitational Anomaly in 4d
text, January 2014

Fermion masses without symmetry breaking in two spacetime dimensions
text, January 2014

State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
text, January 2016

Ising Anyons in Frustration-Free Majorana-Dimer Models
text, January 2016

Anyons in an exactly solved model and beyond
text, January 2005

Spherical 2-categories and 4-manifold invariants
text, January 1998

Fermion decoration construction of symmetry-protected trivial order for fermion systems with any symmetry and in any dimension
journal, December 2019

Disentangling Interacting Symmetry-Protected Phases of Fermions in Two Dimensions
journal, January 2019

A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants
journal, January 2019

Anomalous Symmetry Protected Topological States in Interacting Fermion Systems
journal, November 2019

Fermionic projected entangled-pair states and topological phases
journal, December 2017

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
journal, January 2020

Tunneling topological vacua via extended operators: (Spin-)TQFT spectra and boundary deconfinement in various dimensions
journal, May 2018

Topological nonlinear $σ$ -model, higher gauge theory, and a systematic construction of $3 + 1 D$ topological orders for boson systems
journal, July 2019

Full commuting projector Hamiltonians of interacting symmetry-protected topological phases of fermions
journal, October 2018

Higher-order symmetry-protected topological states for interacting bosons and fermions
text, January 2018

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
text, January 2017

Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
text, January 2017

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
text, January 2017

Symmetry Protected Topological phases and Generalized Cohomology
text, January 2017

Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
text, January 2018

Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
text, January 2018

Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
text, January 2018

Crystalline topological phases as defect networks
text, January 2018

Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
text, January 2018

Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
text, January 2018